Question

A bowling ball of mass 7.29 kg and radius 11.0 cm rolls without slipping down a lane at 3.00 m/s. Calculate the total kinetic energy.

Answer 1

We have the next information

m=7.29 kg

v=3 m/s

r=11cm=0.11m

We can find the kinetic energy using the next formula

`KE=(1)/(2)mv^2+(1)/(2)Iw^2`

I is the moment of inertia

w is the angular velocity

First, we need to calculate the moment of inertia

`I=(2)/(5)mr^2`
`I=(2)/(5)(7.29)(0.11)^2=0.0353kgm^2`

Then for the angular velocity

`\omega=(v)/(r)`

`\omega=(3)/(0.11)=27.28`

then we will substitute the values in the kinetic energy formula

`KE=(1)/(2)(7.29)(3)^2+(1)/(2)(0.0353)(27.28)^2`
`KE=45.9J`

The total kinetic energy is 45.9 J